Power generators, including nuclear reactors, are used for power generation, research and propulsion. A power generation circuit generally includes a heat source such as a nuclear core or furnace and a coolant circuit. For light water reactor, respective coolant piping circuits transport the heated water or steam to either a steam generator and then a turbine, or directly to a turbine, and after going through a condenser (heat sink), carries circulating or feedwater back to the heating source. Operating temperatures and pressure may range up to or above the critical point of water. Depending on the operational conditions, the various materials used must withstand various load, environmental and radiation conditions.
Material used as coolant piping and other circuit and heat source components include but are not limited to carbon steels, stainless steels, nickel-based and other alloy steels and zirconium based alloys. These materials have to withstand the high temperature and high pressure conditions. Although the materials have been carefully selected, corrosion occurs caused by the corrosive nature of the environment: high temperature, high pressure water, steam, water radiolysis, additives in water and radiation effects. Such corrosion processes limit the lifetime of the systems in contact with the coolant fluid, and include but are not limited to stress corrosion cracking, flow accelerated corrosion, crevice corrosion, erosion corrosion, generalized corrosion and nodular corrosion.
Stress corrosion cracking (SCC), including intergranular stress corrosion cracking (IGSCC), is a well-known phenomenon happening to structural components in coolant circuits of a nuclear reactor, which affects the base and welding materials. SCC occurs through crack initiation, and propagation, which are caused by a combination of chemical, tensile and ductile stresses (static and dynamic). Such stresses are common in nuclear environments caused by thermal expansion and contraction, residual stresses from welding, cold working, etc. The susceptibility toward SCC is often increased by the operating coolant environment, welding, heat treatment, radiolysis and radiation.
High oxygen content in the coolant fluid has been shown to accelerate SCC through higher rates of crack initiation and propagation. High oxygen content in the coolant fluid can stem from oxygen intrusion and water radiolysis processes, which create highly oxidizing species such as oxygen radical, hydrogen peroxide and many other radical species in the gamma, neutron, beta, and alpha flux.
Corrosion products present in the coolant fluid ultimately accumulate on the heat transfer surface, for instance on surfaces formed of zirconium of the fuel elements of a nuclear reactor core or on internal surfaces of steam generator tubes made of stainless steel, forming a deposit layer commonly called crud. The structure of the deposit layer varies within its thickness and comprises an outer portion of low density loose crud, harboring mostly water, which is in constant exchange with the circulating reactor water, but providing a metal oxide structure capable of attracting and retaining colloidal particulates. This portion of low density loose crud is called fluffy crud. Below the portion of fluffy crud, closer to the heat transfer surface, the deposit layer comprises a inner portion of higher density crud, called tenacious crud, stuck to the heat transfer surface. The tenacious crud forms on a metal oxide layer of the heat transfer surface, which forms on heat transfer surface due to heating of heat transfer surface (i.e., general corrosion). For example, on fuel element surfaces formed of zirconium, heating results in the increase of a native zirconium oxide layer. The fraction of tenacious crud in the deposit layer increases as crud deposition increases and the crud ages. The densification is accelerated by excessive heat and prolonged exposure to reactor environment.
The sponge-like nature of the deposit layer creates conditions corresponding to capillary water movement. The very low capillary velocities of fluids in crud, creating almost confined conditions, favor the water radiolysis reactions that form the molecular species, i.e. hydrogen, oxygen, hydrogen peroxide and the HO radical. Studies, such as S. Le Caër et al., Hydrogen Peroxide Formation in the Radiolysis of Hydrated Nanoporous Glasses: A Low and High Dose Study, Chem. Phys. Lett. 450 (2007) 91-95, have shown that the hydrogen in confined spaces is ineffective in facilitating the recombination reaction to water. Hence, in confined spaces the sum of the oxidizing species, i.e. oxygen, hydrogen peroxide and oxygen radical, effectively create an oxygen saturated environment.
The amount and form of the deposit layer formed on the heat transfer surfaces depends on the concentrations and types of the chemical elements in the water to be converted to steam. The elements are typically in the form of particulate, colloidal and/or ionic species. As the water is converted to steam, the chemical, physical and thermodynamic processes will work in concert (interactively) to produce the evolution of the deposit layer.
Over the years, there have been a number of efforts to understand and model the evolution of the deposit layer and the resulting heat transfer performance. The deposit typically evolves as a porous layer. Heat transfer through the deposit layer is primarily a combination of conduction through the deposit and water matrix and convection through water in the matrix which is converted to steam.
Theories and models have focused on a concept of small capillaries within the porous matrix that conduct water to larger diameter openings called “steam chimneys,” where the water is converted to steam. The steam then travels from the steam chimney into the coolant fluid convectively transferring the heat of vaporization. A fixed diameter was used to delineate the openings that were assumed to be capillaries and those that were assumed to be steam chimneys. U.S. Pat. No. 7,420,165 teaches a method of calculating the power transfer of a nuclear component based on a number of steam chimneys in a deposit layer on the nuclear component.
Under most conditions, deposits on heat transfer surfaces make the heat transfer less efficient, and increase the potential for thermal or corrosion damage of the heat transfer surface. Modeling efforts provide a better understanding of the deposition phenomenon and thus help in the development of mitigative and corrective actions.
Although some of the earliest models of deposits on heat transfer surfaces treated the deposit as a layer with a modified coefficient of thermal conductivity, it was soon realized that the transfer of heat through a porous deposit layer was much more complex than simple conduction.
Along these lines, the wick heat transfer model was developed. The wick heat transfer model accounted for the fact that heat transfer in a porous deposit is a combination of conductive and convective heat transfer. The conduction is through the deposit matrix and the convection is from the movement and heating of the coolant fluid within the deposit matrix. The primary convective heat transfer is from the movement of coolant fluid into the deposit matrix where it becomes steam and returns to the coolant fluid.
FIG. 1 shows a version of the wick heat transfer model illustrating a deposit layer 10, which has a thickness X on a heat transfer surface 12. Solutes in the flowing coolant fluid 14 are carried into pores formed in the outer surface 16 of deposit layer 10 by a network of small diameter “capillaries” 18 which fed the fluid 14 into “steam chimneys” 20 where the water was able to absorb the latent heat of vaporization and move back into the fluid 14 as steam. The diameter of a given opening within the deposit layer 10 was used to define whether the path would serve as a capillary 18 supplying fluid 14 or as a steam chimney 20 where the fluid 14 was converted to steam. The smaller diameter openings were capable of wicking the fluid into the hotter regions of the deposit layer 10 without boiling. If the fluid from a capillary 18 connects to the larger diameter of a steam chimney 20, the larger flow opening allows the fluid 14 to flash to steam and flow out to the fluid 14. Any deposit surface openings larger than a specific diameter were counted as steam chimneys 20 and empirical relationships were derived to relate the number of steam chimneys 20 to the heat flux capacity of the deposit layer 10.